Arcane Value: Why does it go 1/3 -> 1/2 -> 2/3?

I couldn't find/remember anything explaining this, although it's probably out there, but I felt the urge to ask again. What's the reasoning behind 1 point of arcane value giving 1/3rd instead of 1/4th and, by extension, 3 points giving 2/3rds instead of 3/4ths?

For those following along on the G+ ACKs community, this is an extension of me continuing to ruminate on Zaharan Ruinguards. In my campaign I replaced Zaharans with Tieflings and they still have an active kingdom so they are somewhat more common than in the default setting.

Looking at the tables in Axioms 1, my suspicion is that it is some kind of pro-rating by usefulness.

The different base costs, since they're consistent, can be combined to form a full table of what it costs to have various spellcasting amounts; the ones that have an XP cost multiplier different than their spellcasting multiplier are 1/3 (x0.25,), 2/3 (x0.75), 4/3 (x2), and 3/2 (x4). Interestingly, 2/3 level costs the same as 3/4 level. The fact that they're all 'something thirds' outside of 3/2 makes me think that maybe it's a rounding thing as well.

I might actually have a possible solution to this inspired by the HFH tables. I wonder what would happen if we took the arcane spell point progression for non-4 values of arcane and then converted it back into spells per day following a progression similar to what we would see with actual levels. This includes an accounting for level progression and expected power level of character by making it a weighted average of all spell progression instead of strictly 'what a mage of X% level would have'.

I might actually have a possible solution to this inspired by the HFH tables. I wonder what would happen if we took the arcane spell point progression for non-4 values of arcane and then converted it back into spells per day following a progression similar to what we would see with actual levels. This includes an accounting for level progression and expected power level of character by making it a weighted average of all spell progression instead of strictly 'what a mage of X% level would have'. I'll work up some tables on it at some point.
-Aryxymaraki

I might actually have a possible solution to this inspired by the HFH tables. I wonder what would happen if we took the arcane spell point progression for non-4 values of arcane and then converted it back into spells per day following a progression similar to what we would see with actual levels. This includes an accounting for level progression and expected power level of character by making it a weighted average of all spell progression instead of strictly 'what a mage of X% level would have'. I'll work up some tables on it at some point.

The first thing I noticed was that at some point Alex changed the tables to be consistent with the spell progression of these points instead of being multiplied percentages of full based on their spellcasting percentage >.>

But that's what I did to create these tables, which are preliminary (obviously, given how long they took >.>) but should serve as a proof of concept. In all cases, they're definitely stronger than the existing spell progressions for these values, but should also be still definitely weaker than Arcane4. Arcane1 gets a single fifth-level spell at 14th level; Arcane2 gets their first 5th level spell at 12, but never makes it to 6th; and Arcane3 gets a single sixth level spell when they reach 14th level.

(Determining their effective spellcaster level is much more complicated. I think 'twice the level of the highest-level spell they can cast' is a reasonable approximation, but has a few weird points, so it only works as an approximation.)

The first thing I noticed was that at some point Alex changed the tables to be consistent with the spell progression of these points instead of being multiplied percentages of full based on their spellcasting percentage >.> But that's what I did to create these tables, which are preliminary (obviously, given how long they took >.>) but should serve as a proof of concept. In all cases, they're definitely stronger than the existing spell progressions for these values, but should also be still definitely weaker than Arcane4. Arcane1 gets a single fifth-level spell at 14th level; Arcane2 gets their first 5th level spell at 12, but never makes it to 6th; and Arcane3 gets a single sixth level spell when they reach 14th level. I can't post tables here so here's a link! http://aryxymaraki.pbworks.com/w/page/121906002/Alternate%20Progression%... (Determining their effective spellcaster level is much more complicated. I think 'twice the level of the highest-level spell they can cast' is a reasonable approximation, but has a few weird points, so it only works as an approximation.)
-Aryxymaraki

These are awesome. Can we publish them as an AXIOMS article? Along with updated spell point tables.

The first thing I noticed was that at some point Alex changed the tables to be consistent with the spell progression of these points instead of being multiplied percentages of full based on their spellcasting percentage >.> But that's what I did to create these tables, which are preliminary (obviously, given how long they took >.>) but should serve as a proof of concept. In all cases, they're definitely stronger than the existing spell progressions for these values, but should also be still definitely weaker than Arcane4. Arcane1 gets a single fifth-level spell at 14th level; Arcane2 gets their first 5th level spell at 12, but never makes it to 6th; and Arcane3 gets a single sixth level spell when they reach 14th level. I can't post tables here so here's a link! http://aryxymaraki.pbworks.com/w/page/121906002/Alternate%20Progression%... (Determining their effective spellcaster level is much more complicated. I think 'twice the level of the highest-level spell they can cast' is a reasonable approximation, but has a few weird points, so it only works as an approximation.)

-Aryxymaraki

These are awesome. Can we publish them as an AXIOMS article? Along with updated spell point tables.

-Alex

Of course!

I will try to polish the tables a bit more, maybe figure out the caster level conondrum and send it to you.

How would this work for Divine 1/2? I would really like to see it as I'm experimenting with building a paladin type caster class.

-Chimera_Prime

The math is the same for Divine 1. HFH has the spell point values by level for Divine 2; you'd just take that, multiply by the multiplier for Divine 1, and convert it back into spells per day.

For Divine 3 and 4, it doesn't follow strictly the multiplier, because Divine 4 gets a spell at first level. So I'd have to look into it to be able to give an answer. But Divine 1, at least, can be done with the same method.

Divine 1 progression on p.102 HFH seems to add points in the mid levels where you dont get spells.

Either way its replaced with a cap of 84/2 = 42.

Divine progression is wierd, I tried not to give more spells in any level than divine 1. Some levels come under points and some over. And divine half still gets 5th level so i kept that in. I also used Alex's caster level formula.

Without actually redoing the math, just a quick once-over, yup, that looks pretty similar to the methodology I used.

The Axioms article has the more finalized arcane progressions to use as an example (I actually can't remember 100% what changes there were to the preliminary versions, but they have caster level listed at least), along with more explanation of the method and the delayed acqusiition versions/methods.

Divine progression is definitely weird, and for your own campaign, the only thing I'd worry about is whether or not it works for you.

The Divine progression was based on the one used in B/X. The main thing it does, compared to a more regular progression, is bring magic capable of restoring the dead to life from life at level 7 instead of level 9. Since that was an important in gameplay, I left it as-is.